Further results on a generalization of Bertrand's postulate

Abstract

Let d(k) be defined as the least positive integer n for which pn+1<2pn−k. In this paper we will show that for k≥286664, then d(k)<k/(logk−2.531) and for k≥2, then k(1−1/logk)/logk<d(k). Furthermore, for k sufficiently large we establish upper and lower bounds for d(k).